K2OWK--The answer is simple--to a point. Some of the radio receivers made in the past that have bakelite cases and knobs--that is that have the chassis completely shielded from the user's touch--have one side of the power cord tied to the chassis. Get and refer to a schematic of the radio in question if you can to determine that.
The trick is to find out where that tie-in is--if you're unable to get a schematic. HOWEVER, note that in some of those radios, that connection MUST BE THERE in order for the radio to operate properly. That is why some advocate leaving the two wire cord alone.
What has to be done is to meter each side of the power cord--with the switch for the receiver off--to the chassis itself. If you find a dead short, then look for that connection and temporarily open it. If there is still some continuity between chassis and the cord connections after that connection is opened, you cannot use a three wire power cord safely, you have to use a two wire cord. Using a three wire cord in that instance could put 110 volts on the third wire of that house circuit, and if the third wire of that circuit was open anywhere between the outlets and the panel, could make other appliances connected to that circuit with a three wire cord a shock hazard in themselves!
If, on the other hand, you find no continuity at all or can effectively isolate the chassis from both sides of the power line and still have the receiver work properly, you can use a three wire cord safely. Please note that I'm speaking of 110 volt US connections--220 volt and other foreign electrical systems do vary.
On a lighter note--sometimes it's nice to be an old fart, having the knowledge to help out others! 73!